The time-dependent Born-Oppenheimer approximation
Panati, Gianluca ; Spohn, Herbert ; Teufel, Stefan1
1 Mathematisches Institut, Universität Tübingen, Germany. stefan.teufel@uni-tuebingen.de
ESAIM: Modélisation mathématique et analyse numérique, Special issue on Molecular Modelling, Tome 41 (2007) no. 2, pp. 297-314.

We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for higher order corrections. We also present a new elementary derivation of the correct second-order time-dependent Born-Oppenheimer approximation and discuss as applications the dynamics near a conical intersection of potential surfaces and reactive scattering.

DOI : 10.1051/m2an:2007023
Classification : 81Q05, 81Q15, 81Q70
Mots-clés : Schrödinger equation, Born-Oppenheimer approximation, adiabatic methods, almost-invariant subspace
Panati, Gianluca  ; Spohn, Herbert  ; Teufel, Stefan 1

1 Mathematisches Institut, Universität Tübingen, Germany. stefan.teufel@uni-tuebingen.de 
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Panati, Gianluca; Spohn, Herbert; Teufel, Stefan. The time-dependent Born-Oppenheimer approximation. ESAIM: Modélisation mathématique et analyse numérique, Special issue on Molecular Modelling, Tome 41 (2007) no. 2, pp. 297-314. doi : 10.1051/m2an:2007023. http://www.numdam.org/articles/10.1051/m2an:2007023/

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